Question

Вычислите
$(2 log_{25}1,6 - log_{5}8 + 3) \times 6 {}^{2 log_{6}3 }$
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Answer 1

Решение:

$(2log_{25}1,6-log_{5}8+3)*6^{2log_{6}3}=(2log_{5^{2} }1,6-log_{5}8+3)*6^{log_{6}3^{2}}=(2*\frac{1}{2}*log_{5}1,6-log_{5}8+3)*3^{2}=(log_{5}1,6-log_{5}8+3)*9=9log_{5}1,6-9log_{5}8+27=log_{5}1,6^{9}+log_{5}8^{-9}+27=log_{5}(1,6^{9}*8^{-9})+27=log_{5}((\frac{8}{5})^{9}*\frac{1}{8^{9}})+27=log_{5}(\frac{\frac{8^{9}}{5^{9}}}{8^{9}})+27=log_{5}(\frac{1}{5^{9}})+27=log_{5}(5^{-9})+27=-9+27=18$

Ответ: 18